OFFSET
1,2
COMMENTS
In these trees, achiral means that all branches directly under any given node that is not a leaf or a cover of leaves are equal, and series-reduced means that every node that is not a leaf or a cover of leaves has at least two branches.
EXAMPLE
The a(4) = 9 trees:
(1111), ((11)(11)), (((1)(1))((1)(1))), ((1)(1)(1)(1)),
(1112),
(1122), ((12)(12)),
(1123),
(1234).
The a(6) = 19 trees:
(111111), ((111)(111)), (((1)(1)(1))((1)(1)(1))), ((11)(11)(11)), (((1)(1))((1)(1))((1)(1))), ((1)(1)(1)(1)(1)(1)),
(111112),
(111122), ((112)(112)),
(111123),
(111222), ((12)(12)(12)),
(111223),
(111234),
(112233), ((123)(123)),
(112234),
(112345),
(123456).
MATHEMATICA
b[n_]:=1+Sum[b[n/d], {d, Rest[Divisors[n]]}];
a[n_]:=Sum[b[GCD@@Length/@Split[ptn]], {ptn, IntegerPartitions[n]}];
Array[a, 30]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 01 2018
STATUS
approved